Senators are moving forward with legislation that would curb President TrumpDonald John TrumpWhite House counsel called Trump 'King Kong' behind his back: report Trump stays out of Arizona's ugly and costly GOP fight Trump claims he instructed White House counsel to cooperate with Mueller MORE's authority on tariffs, despite opposition from the White House.

"If the president truly believes invoking Section 232 is necessary to protect the United States from a genuine threat, he should make the case to Congress and to the American people and do the hard work necessary to secure congressional approval," Sen. Bob CorkerRobert (Bob) Phillips CorkerSen. Warner to introduce amendment limiting Trump’s ability to revoke security clearances White House weighs clawing back State, foreign aid funding Rand Paul to ask Trump to lift sanctions on Russian leaders MORE (R-Tenn.) said in a statement announcing the bill.

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In addition to Corker, Sens. Heidi HeitkampMary (Heidi) Kathryn HeitkampThe Hill's Morning Report: Dems have a majority in the Senate (this week) Overnight Health Care: Supreme Court nomination reignites abortion fight in states | Trump urges Sessions to sue opioid makers | FDA approves first generic version of EpiPen Judge rules against Trump attempt to delay Obama water rule MORE (D-N.D.), Pat ToomeyPatrick (Pat) Joseph ToomeyOvernight Defense: Pick for South Korean envoy splits with Trump on nuclear threat | McCain blasts move to suspend Korean military exercises | White House defends Trump salute of North Korean general WH backpedals on Trump's 'due process' remark on guns Top GOP candidate drops out of Ohio Senate race MORE (R-Pa.), Mark WarnerMark Robert WarnerSenators demand answers on reported lead poisoning at Army bases Top Republican: Senate panel not ready to wrap up Russia probe The Memo: For Trump, this week has been anything but sleepy MORE (D-Va.), Lamar AlexanderAndrew (Lamar) Lamar AlexanderGovernor's race grabs spotlight in Tennessee primaries A single courageous senator can derail the Trump administration GOP worries trade wars will last as Trump engages in temporary tiffs MORE (R-Tenn.), Brian SchatzBrian Emanuel SchatzGOP leader criticizes Republican senators for not showing up to work Senate takes shot at Trump, passes resolution affirming 'press is not the enemy of the people' Pentagon’s No. 2 official: Trump’s ‘Space Force’ could cost 'billions' MORE (D-Hawaii), Ron JohnsonRonald (Ron) Harold JohnsonSunday shows preview: Trump stokes intel feud over clearances Rand Paul to ask Trump to lift sanctions on Russian leaders Hillicon Valley: Twitter CEO Jack Dorsey sits down with The Hill | Drama over naming DHS cyber office | Fallout over revoking Brennan's security clearance | Google workers protest censored search engine for China MORE (R-Wis.), Chris Van HollenChristopher (Chris) Van HollenDem campaign chairman expresses confidence over path to Senate majority Trump draws bipartisan fire over Brennan New sanctions would hurt Russia — but hurt American industry more MORE (D-Md.), Mike LeeMichael (Mike) Shumway LeeSentencing reform deal heats up, pitting Trump against reliable allies Senate gets to work in August — but many don’t show up GOP leader criticizes Republican senators for not showing up to work MORE (R-Utah), Jeff FlakeJeffrey (Jeff) Lane FlakeTrump stays out of Arizona's ugly and costly GOP fight Voters will punish Congress for ignoring duty on war and peace GOP Senate candidate truncates Trump tweet in campaign mailer MORE (R-Ariz.), Ben SasseBenjamin (Ben) Eric SassePollster: Attitudes toward Trump's farm aid are 'highly wrapped up' in feelings toward president Poll: Majority of Americans support Trump's plan to offer aid to farmers hit by tariffs Hillicon Valley: 'QAnon' conspiracy theory jumps to primetime | Senate Intel broadens look into social media manipulation | Senate rejects push for more election security funds | Reddit reveals hack MORE (R-Neb.) and Johnny IsaksonJohn (Johnny) Hardy IsaksonSenators demand answers on reported lead poisoning at Army bases Overnight Defense: Questions mount over Trump's Iran tweet | House, Senate unveil compromise defense bill | Bill includes Russia sanctions waivers, limits on Turkey's access to F-35 | Endangered species measures dropped Senate confirms Trump's VA pick despite opposition from some Dems MORE (R-Ga.) are supporting the bill.

"There is no real national security threat that these tariffs are a response to. They are an effort to impose a protectionist policy for economic purposes," Toomey said in a floor speech blasting the administration's decisions.

The bill would require Trump to submit tariffs implemented under Section 232 of the trade law for approval to Congress. Any approval legislation would then be fast-tracked through both chambers.

Senators are introducing the legislation despite receiving pushback from Trump, who earlier on Wednesday privately urged Corker not to file his bill.

“I talked at length with the president about it today. He's obviously not pleased with this effort,” Corker separately told reporters.

Corker added that Trump's main message in the phone call, which the president initiated, was for Corker to not move forward with the proposal.

But congressional Republicans are becoming increasingly frustrated with Trump's trade policy, which they worry could roil the economy just months before a midterm election. 

The administration ratcheted up long-simmering tensions late last week when they announced that they would subject steel and aluminum imports from Canada, Mexico and the European Union to steep tariffs, ending an exemption for the trading allies.

A group of GOP senators met with Trump on Wednesday at the White House to discuss trade. The meeting was organized by GOP Sen. Lindsey GrahamLindsey Olin GrahamSenate gets to work in August — but many don’t show up Graham: Flynn should lose security clearance Press needs to restore its credibility on the FBI and Justice Department MORE (S.C.).

“I think Sen. Graham, who is the leader of that meeting, just wants to talk to the president about his end game,” Sen. John CornynJohn CornynSen. Warner to introduce amendment limiting Trump’s ability to revoke security clearances Sentencing reform deal heats up, pitting Trump against reliable allies Rand Paul to ask Trump to lift sanctions on Russian leaders MORE (R-Texas) told reporters when asked about the meeting.

Graham said after the closed-door meeting that Trump is "on track to get us better trade deals" and signaled he will oppose Corker's legislation.

“Now is not the time to undercut President Trump’s ability to negotiate better trade deals. I will not support any efforts that weaken his position," Graham said in a statement.

Notably missing from the supporters of Corker's bill are members of Senate GOP leadership.

Some GOP senators are wary of picking a fight with Trump, saying lawmakers should focus on trying to change the president’s mind. 

"I'm not sure right at this particular time it's advisable. ... My preference would be to convince the president that perhaps he should take a different approach," Sen. Pat RobertsCharles (Pat) Patrick RobertsThe farm bill gives Congress a chance to act on the Pet and Women Safety (PAWS) Act Kobach secures GOP nomination in hotly contested Kansas governor's race GOP senators surprised to attend Trump’s tariffs announcement MORE (R-Kan.) told reporters. 

Pressed if that strategy was working, Roberts acknowledged, "to date, no." 

Sen. John KennedyJohn Neely KennedyMORE (R-La.) added that while he is reviewing Corker's legislation, he still believes "that the president is too smart to start a trade war." 

Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellTrump stays out of Arizona's ugly and costly GOP fight Sen. Warner to introduce amendment limiting Trump’s ability to revoke security clearances The Hill's 12:30 Report MORE (R-Ky.) told reporters on Tuesday that he would not bring up the tariff legislation as a stand-alone bill but noted the National Defense Authorization Act (NDAA) was open to amendment.

“I'm not going to call it up free-standing. You're suggesting it might be offered as an amendment. NDAA's going to be opened, we'll see what amendments are offered,” McConnell said, asked about Corker's bill.

Corker has pointed to the NDAA as one potential vehicle for his tariff legislation. But getting the bill brought up as an amendment to the defense policy bill would require the consent of every senator.

Sen. James InhofeJames (Jim) Mountain InhofePence announces first steps in establishing 'Space Force' EPA chief: Obama car rule rollback would save consumers 0B EPA’s Wheeler gets warmer welcome at Senate hearing MORE (R-Okla.), who is managing the bill in the absence of Armed Services Committee Chairman John McCainJohn Sidney McCainThe Hill's 12:30 Report Senate gets to work in August — but many don’t show up Rand Paul’s Russia visit displays advancement of peace through diplomacy MORE (R-Ariz.), said he thought Corker would ultimately be able to get a vote. 

"I think it will. In fact, I told Corker that I would not object to it," Inhofe said, while noting he would vote against the amendment. 

Asked if he thought Corker's bill should get a vote as part of the NDAA, Cornyn said the Senate should have an "open amendment process." 

"It's the source of a lot of frustration here among members when people are denied an opportunity to vote. Back in the good old days ... we used to have [a] much more open amendment process," he said. 

But the process for setting up roll call votes on amendments to the NDAA has ground to a halt in recent years as senators object to a vote on any amendment unless they can also get a vote on their own proposals.

Cornyn noted on Wednesday that there are already objections to amendments as lawmakers jockey for leverage, which could complicate Corker's quest to add his tariff legislation to the defense policy bill.

Business groups, considered a long-standing ally of Republicans, quickly backed Corker's bill.

Neil Bradley, the executive vice president and chief policy officer for the Chamber of Commerce, said on Wednesday that there was concern that Trump's tariff decision would cost American jobs. 

"The constitutional authority of the Congress to 'regulate foreign trade' and its oversight of tariff policy is unambiguous. The modest proposal to clarify congressional prerogatives is welcome and long overdue," Bradley added.

There is no sign that the House is prepared to introduce similar legislation. Asked about the tariff legislation on Wednesday, Speaker Paul RyanPaul Davis RyanNew Dem ad uses Paterno, KKK, affair allegations to tar GOP leaders House Dem: Party's aging leaders is 'a problem' Rand Paul to ask Trump to lift sanctions on Russian leaders MORE (Wis.) noted that Trump would have to sign the bill.

“You would have to pass a law that he would want to sign into law,” he told reporters. “You can do the math on that.”

Updated at 7:03 p.m.